1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Pascals triangle problem(discrete mathematics)

  1. Oct 28, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine which row of pascals triangle contains 3 consecutive entries that are in the ratio 1:2:3.

    2. Relevant equations
    (n, k ) = n!/k!(n-k)!

    3. The attempt at a solution
    1 : 2: : 3

    What I did was cross multiply.

    2 times (n,k) = 1 times (n,k+1) and 3 times (n,k+1) = 2 times (n,k+2)
    2(n!/(k!(n-k)!) = n!/(k+1)!(n-k-1)! and 3(n!/(k+1)!(n-k-1)!) = 2(n!/(k+2)!(n-k-2)!

    I know that i should solve for n in the first equation then substitute n in the second equation to get n and k. I'm stuck on the algebra part.
  2. jcsd
  3. Oct 28, 2012 #2


    User Avatar
    Homework Helper

    Well, what are some of the rules of factorials?

    n! = n*(n-1)*(n-2)*...*2*1

    n! = n*(n-1)!

    So if we have an equation such as

    n! = 10*(n-1)!

    then to solve this, we would use the rule n! = n*(n-1)! to obtain

    n*(n-1)! = 10*(n-1)!

    then you can divide through by (n-1)! and find n=10. See if you can apply this rule to solve your equation.
  4. Oct 30, 2012 #3
    thank you i got the answer.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook